The burn rate for the Falcon 9 first stage is 162 seconds. In order to get 162 seconds from this calculation, it requires a velocity of 4176 m/sec / 15033.6 km/h which is absurd. The latest launch, Telstar 18 reached 8162 km/h at 'meco' nearly HALF. I know that they throttle down for max-q.

Is the missing element gravity losses? I'm not seeing them in the equation. Any thrust directed down has to fight gravity as well as accelerate the rocket. Subtract 9.8 m/s per second of thrust -- but this only applies to the vertical component, not the horizontal.
– SaibooguSep 14 at 15:42

"The burn rate for the Falcon 9 first stage is 162 seconds" This makes no sense. Burn rates are not measured in seconds.
– Organic MarbleSep 14 at 16:10

The title of 162 second FT is "Burn time". I am looking to find out how they calculate the 162 second amount from the first stage
– UndefinedUsernameSep 14 at 16:16

That does leave the throttle schedule as an unknown; if you're still trying to figure out the "actual" launch mass of the Falcon 9, this is going to be another dead end for you.

Assuming 410900 kg of propellant in the first stage, full-throttle burn would empty the stage in 410900 / (9 x 305.1) = 149.6 seconds. The throttle-down extends the burn time by 12 seconds.

The "expended velocity" figure you computed of 4176 m/s is reasonable, incidentally. Circular LEO velocity is about 7800 m/s, but ascent from Earth's surface to LEO takes roughly 9300-9700 m/s of expended ∆v (varying with the ascent trajectory and the size of the launcher) because of gravity, arc, and drag losses. The first stage pays for the vast majority of the 1500-1900 m/s difference. So you'd expect the 4176 m/s of expended ∆v to yield a linear velocity in the ballpark of 2500 m/s, or 9000 kph.